We have derived the near-infrared structural components of a sample of Seyfert and starburst (SBN) host galaxies by fitting near-infrared images with a new two-dimensional decomposition algorithm. An analysis of the fitted parameters shows that Seyfert 1 and SBN bulges resemble normal early-type bulges in structure and color, with (J-K)^c^b about 0.1 mag redder than disk (J-K)^c^d. Seyfert 2 bulges, on the other hand, are bluer than normal, with (J-K)^c^b{approx}(J-K)^c^d. Seyfert disks (especially type 1), but not those of SBNs, are abnormally bright (in surface brightness), significantly more so than even the brightest normal disks. Seyfert disks are also compact, but similar to those in normal early-type spirals. For a given mass, Seyfert and particularly SBN galaxies are abnormally rich in neutral hydrogen, and there is strong, albeit indirect, evidence for lower mass-to-light (M/L) ratios in Seyfert and SBN disks, but normal M/L ratios in their bulges. In Seyfert and SBN galaxies, H I mass fractions and M/L ratios are anticorrelated, and we attribute the high gas mass fractions and low M/L ratios in SBNs and several Seyfert galaxies to ongoing star formation. Such abundant gas in Seyfert galaxies would be expected to inhibit bar formation, which may explain why active galaxies are not always barred.